6.5: The Effects of Public Opinion
-
- Last updated
- Save as PDF
Learning Objectives
By the end of this section, you will be able to:
- Explain the circumstances that lead to public opinion affecting policy
- Compare the effects of public opinion on government branches and figures
- Identify situations that cause conflicts in public opinion
Public opinion polling is prevalent even outside election season. Are politicians and leaders listening to these polls, or is there some other reason for them? Some believe the increased collection of public opinion is due to growing support of delegate representation. The theory of delegate representation assumes the politician is in office to be the voice of the people. 90 If voters want the legislator to vote for legalizing marijuana, for example, the legislator should vote to legalize marijuana. Legislators or candidates who believe in delegate representation may poll the public before an important vote comes up for debate in order to learn what the public desires them to do.
Regardless of why the polls are taken, studies have not clearly shown whether the branches of government consistently act on them. Some branches appear to pay closer attention to public opinion than other branches, but events, time periods, and politics may change the way an individual or a branch of government ultimately reacts.
Public Opinion and Elections
Elections are the events on which opinion polls have the greatest measured effect. Public opinion polls do more than show how we feel on issues or project who might win an election. The media use public opinion polls to decide which candidates are ahead of the others and therefore of interest to voters and worthy of interview. From the moment President Obama was inaugurated for his second term, speculation began about who would run in the 2016 presidential election. Within a year, potential candidates were being ranked and compared by a number of newspapers. 92 The speculation included favorability polls on Hillary Clinton, which measured how positively voters felt about her as a candidate. The media deemed these polls important because they showed Clinton as the frontrunner for the Democrats in the next election. 93
During presidential primary season, we see examples of the bandwagon effect, in which the media pays more attention to candidates who poll well during the fall and the first few primaries. Bill Clinton was nicknamed the “Comeback Kid” in 1992, after he placed second in the New Hampshire primary despite accusations of adultery with Gennifer Flowers. The media’s attention on Clinton gave him the momentum to make it through the rest of the primary season, ultimately winning the Democratic nomination and the presidency.
Link to Learning
Wondering how your favorite candidate is doing in the polls? The site RealClearPolitics tracks a number of major polling sources on the major elections, including the presidential and Senate elections.
Polling is also at the heart of horserace coverage , in which, just like an announcer at the racetrack, the media calls out every candidate’s move throughout the presidential campaign. It often includes near-constant reporting on polls (some of which have questionable validity), accompanied by commentary from election experts or spokespeople for the candidates. Sound bites, tweets, and video of campaign stops are frequently integrated into this somewhat surface-level reporting. Horserace coverage can be neutral, positive, or negative, depending upon what polls or facts are covered (Figure 6.16). During the 2012 presidential election, the Pew Research Center found that both Mitt Romney and President Obama received more negative than positive horserace coverage, with Romney’s growing more negative as he fell in the polls. 94 Horserace coverage is often criticized for its lack of depth; the stories skip over the candidates’ issue positions, voting histories, and other facts that would help voters make an informed decision. Yet, horserace coverage is popular because the public is always interested in who will win, and it often makes up a third or more of news stories about the election. 95 Exit polls, taken the day of the election, are the last election polls conducted by the media. Announced results of these surveys can deter voters from going to the polls if they believe the election has already been decided.
Finding a Middle Ground
Should Exit Polls Be Banned?
Exit polling seems simple. An interviewer stands at a polling place on Election Day and asks people how they voted. But the reality is different. Pollsters must select sites and voters carefully to ensure a representative and random poll. Some people refuse to talk and others may lie. The demographics of the polled population may lean more towards one party than another. Absentee and early voters cannot be polled. Despite these setbacks, exit polls are extremely interesting and controversial, because they provide early information about which candidate is ahead.
In 1985, a so-called gentleman’s agreement between the major networks and Congress kept exit poll results from being announced before a state’s polls closed. 96 This tradition has largely been upheld, with most media outlets waiting until 7 p.m. or later to disclose a state’s returns. Internet and cable media, however, have not always kept to the agreement. Sources like Matt Drudge have been accused of reporting early, and sometimes incorrect, exit poll results.
On one hand, delaying results may be the right decision. Studies suggest that exit polls can affect voter turnout. Reports of close races may bring additional voters to the polls, whereas apparent landslides may prompt people to stay home. Other studies note that almost anything, including bad weather and lines at polling places, dissuades voters. Ultimately, it appears exit poll reporting affects turnout by up to 5 percent. 97
On the other hand, limiting exit poll results means major media outlets lose out on the chance to share their carefully collected data, leaving small media outlets able to provide less accurate, more impressionistic results. And few states are affected anyway, since the media invest only in those where the election is close. Finally, an increasing number of voters are now voting up to two weeks early, and these numbers are updated daily without controversy.
What do you think? Should exit polls be banned? Why or why not?
Public opinion polls also affect how much money candidates receive in campaign donations. Donors assume public opinion polls are accurate enough to determine who the top two to three primary candidates will be, and they give money to those who do well. Candidates who poll at the bottom will have a hard time collecting donations, increasing the odds that they will continue to do poorly. This was apparent in the run-up to the 2016 presidential election. Bernie Sanders, Hillary Clinton, and Martin O’Malley each campaigned in the hope of becoming the Democratic presidential nominee. In June 2015, 75 percent of Democrats likely to vote in their state primaries said they would vote for Clinton, while 15 percent of those polled said they would vote for Sanders. Only 2 percent said they would vote for O’Malley. 98 During this same period, Clinton raised $47 million in campaign donations, Sanders raised $15 million, and O’Malley raised $2 million. 99 By September 2015, 23 percent of likely Democratic voters said they would vote for Sanders, 100 and his summer fundraising total increased accordingly. 101
Presidents running for reelection also must perform well in public opinion polls, and being in office may not provide an automatic advantage. Americans often think about both the future and the past when they decide which candidate to support. 102 They have three years of past information about the sitting president, so they can better predict what will happen if the incumbent is reelected. That makes it difficult for the president to mislead the electorate. Voters also want a future that is prosperous. Not only should the economy look good, but citizens want to know they will do well in that economy. 103 For this reason, daily public approval polls sometimes act as both a referendum of the president and a predictor of success.
Public Opinion and Government
The relationship between public opinion polls and government action is murkier than that between polls and elections. Like the news media and campaign staffers, members of the three branches of government are aware of public opinion. But do politicians use public opinion polls to guide their decisions and actions?
The short answer is “sometimes.” The public is not perfectly informed about politics, so politicians realize public opinion may not always be the right choice. Yet many political studies, from the American Voter in the 1920s to the American Voter Revisited in the 2000s, have found that voters behave rationally despite having limited information. Individual citizens do not take the time to become fully informed about all aspects of politics, yet their collective behavior and the opinions they hold as a group make sense. They appear to be informed just enough, using preferences like their political ideology and party membership, to make decisions and hold politicians accountable during an election year.
Overall, the collective public opinion of a country changes over time, even if party membership or ideology does not change dramatically. As James Stimson’s prominent study found, the public’s mood, or collective opinion, can become more or less liberal from decade to decade. While the initial study on public mood revealed that the economy has a profound effect on American opinion, 104 further studies have gone beyond to determine whether public opinion, and its relative liberalness, in turn affect politicians and institutions. This idea does not argue that opinion never affects policy directly, rather that collective opinion also affects the politician’s decisions on policy. 105
Individually, of course, politicians cannot predict what will happen in the future or who will oppose them in the next few elections. They can look to see where the public is in agreement as a body. If public mood changes, the politicians may change positions to match the public mood. The more savvy politicians look carefully to recognize when shifts occur. When the public is more or less liberal, the politicians may make slight adjustments to their behavior to match. Politicians who frequently seek to win office, like House members, will pay attention to the long- and short-term changes in opinion. By doing this, they will be less likely to lose on Election Day. 106 Presidents and justices, on the other hand, present a more complex picture.
Public opinion of the president is different from public opinion of Congress. Congress is an institution of 535 members, and opinion polls look at both the institution and its individual members. The president is both a person and the head of an institution. The media pays close attention to any president’s actions, and the public is generally well informed and aware of the office and its current occupant. Perhaps this is why public opinion has an inconsistent effect on presidents’ decisions. As early as Franklin D. Roosevelt’s administration in the 1930s, presidents have regularly polled the public, and since Richard Nixon’s term (1969–1974), they have admitted to using polling as part of the decision-making process.
Presidential responsiveness to public opinion has been measured in a number of ways, each of which tells us something about the effect of opinion. One study examined whether presidents responded to public opinion by determining how often they wrote amicus briefs and asked the court to affirm or reverse cases. It found that the public’s liberal (or non-liberal) mood had an effect, causing presidents to pursue and file briefs in different cases. 107 But another author found that the public’s level of liberalness is ignored when conservative presidents, such as Ronald Reagan or George W. Bush, are elected and try to lead. In one example, our five most recent presidents’ moods varied from liberal to non-liberal, while public sentiment stayed consistently liberal. 108 While the public supported liberal approaches to policy, presidential action varied from liberal to non-liberal.
Overall, it appears that presidents try to move public opinion towards personal positions rather than moving themselves towards the public’s opinion. 109 If presidents have enough public support, they use their level of public approval indirectly as a way to get their agenda passed. Immediately following Inauguration Day, for example, the president enjoys the highest level of public support for implementing campaign promises. This is especially true if the president has a mandate , which is more than half the popular vote. Barack Obama’s recent 2008 victory was a mandate with 52.9 percent of the popular vote and 67.8 percent of the Electoral College vote. 110 In contrast, President Donald Trump’s victory over Democratic nominee Hillary Clinton was a closer contest. While Clinton outdistanced him by 2.9 million votes nationally, after narrowly winning several states, Trump won a comfortable majority in the Electoral College. By the above definition, Democratic nominee Joe Biden's win over President Trump in 2020 was a mandate. Biden garnered 51.3 percent of the total votes cast, against Trump's 47 percent, and captured 306 Electoral College votes, winning by the same comfortable margin that Trump had four years earlier.
When presidents have high levels of public approval, they are likely to act quickly and try to accomplish personal policy goals. They can use their position and power to focus media attention on an issue. This is sometimes referred to as the bully pulpit approach. The term “bully pulpit” was coined by President Theodore Roosevelt, who believed the presidency commanded the attention of the media and could be used to appeal directly to the people. Roosevelt used his position to convince voters to pressure Congress to pass laws.
Increasing partisanship has made it more difficult for presidents to use their power to get their own preferred issues through Congress, however, especially when the president’s party is in the minority in Congress. 111 For this reason, modern presidents may find more success in using their popularity to increase media and social media attention on an issue. Even if the president is not the reason for congressional action, they can cause the attention that leads to change. 112
Presidents may also use their popularity to ask the people to act. In October 2015, following a shooting at Umpqua Community College in Oregon, President Obama gave a short speech from the West Wing of the White House (Figure 6.17). After offering his condolences and prayers to the community, he remarked that prayers and condolences were no longer enough, and he called on citizens to push Congress for a change in gun control laws. President Obama had proposed gun control reform following the 2012 shooting at Sandy Hook Elementary in Connecticut, but it did not pass Congress. This time, the president asked citizens to use gun control as a voting issue and push for reform via the ballot box.
In some instances, presidents may appear to directly consider public opinion before acting or making decisions. In 2013, President Obama announced that he was considering a military strike on Syria in reaction to the Syrian government’s illegal use of sarin gas on its own citizens. Despite agreeing that this chemical attack on the Damascan suburbs was a war crime, the public was against U.S. involvement. Forty-eight percent of respondents said they opposed airstrikes, and only 29 percent were in favor. Democrats were especially opposed to military intervention. 113 President Obama changed his mind and ultimately allowed Russian president Vladimir Putin to negotiate Syria’s surrender of its chemical weapons.
However, further examples show that presidents do not consistently listen to public opinion. After taking office in 2009, President Obama did not order the closing of Guantanamo Bay prison, even though his proposal to do so had garnered support during the 2008 election. President Bush, despite growing public disapproval for the war in Iraq, did not end military support in Iraq after 2006. And President Bill Clinton, whose White House pollsters were infamous for polling on everything, sometimes ignored the public if circumstances warranted. 114 In 1995, despite public opposition, Clinton guaranteed loans for the Mexican government to help the country out of financial insolvency. He followed this decision with many speeches to help the American public understand the importance of stabilizing Mexico’s economy. Individual examples like these make it difficult to persuasively identify the direct effects of public opinion on the presidency.
While presidents have at most only two terms to serve and work, members of Congress can serve as long as the public returns them to office. We might think that for this reason public opinion is important to representatives and senators, and that their behavior, such as their votes on domestic programs or funding, will change to match the expectation of the public. In a more liberal time, the public may expect to see more social programs. In a non-liberal time, the public mood may favor austerity, or decreased government spending on programs. Failure to recognize shifts in public opinion may lead to a politician’s losing the next election. 115
House of Representatives members, with a two-year term, have a more difficult time recovering from decisions that anger local voters. And because most representatives continually fundraise, unpopular decisions can hurt their campaign donations. For these reasons, it seems representatives should be susceptible to polling pressure. Yet one study, by James Stimson, found that the public mood does not directly affect elections, and shifts in public opinion do not predict whether a House member will win or lose. These elections are affected by the president on the ticket, presidential popularity (or lack thereof) during a midterm election, and the perks of incumbency, such as name recognition and media coverage. In fact, a later study confirmed that the incumbency effect is highly predictive of a win, and public opinion is not. 116 In spite of this, we still see policy shifts in Congress, often matching the policy preferences of the public. When the shifts happen within the House, they are measured by the way members vote. The study’s authors hypothesize that House members alter their votes to match the public mood, perhaps in an effort to strengthen their electoral chances. 117
The Senate is quite different from the House. Senators do not enjoy the same benefits of incumbency, and they win reelection at lower rates than House members. Yet, they do have one advantage over their colleagues in the House: Senators hold six-year terms, which gives them time to engage in fence-mending to repair the damage from unpopular decisions. In the Senate, Stimson’s study confirmed that opinion affects a senator’s chances at reelection, even though it did not affect House members. Specifically, the study shows that when public opinion shifts, fewer senators win reelection. Thus, when the public as a whole becomes more or less liberal, new senators are elected. Rather than the senators shifting their policy preferences and voting differently, it is the new senators who change the policy direction of the Senate. 118
Beyond voter polls, congressional representatives are also very interested in polls that reveal the wishes of interest groups and businesses. If AARP, one of the largest and most active groups of voters in the United States, is unhappy with a bill, members of the relevant congressional committees will take that response into consideration. If the pharmaceutical or oil industry is unhappy with a new patent or tax policy, its members’ opinions will have some effect on representatives’ decisions, since these industries contribute heavily to election campaigns.
Link to Learning
The website of the Policy Agendas Project details a National Science Foundation-funded policy project to provide data on public opinion, presidential public approval, and a variety of governmental measures of activity. All data are coded by policy topic, so you can look for trends in a policy topic of interest to you to see whether government attention tracks with public opinion.
There is some disagreement about whether the Supreme Court follows public opinion or shapes it. The lifetime tenure the justices enjoy was designed to remove everyday politics from their decisions, protect them from swings in political partisanship, and allow them to choose whether and when to listen to public opinion. More often than not, the public is unaware of the Supreme Court’s decisions and opinions. When the justices accept controversial cases, the media tune in and ask questions, raising public awareness and affecting opinion. But do the justices pay attention to the polls when they make decisions?
Studies that look at the connection between the Supreme Court and public opinion are contradictory. Early on, it was believed that justices were like other citizens: individuals with attitudes and beliefs who would be affected by political shifts. 119 Later studies argued that Supreme Court justices rule in ways that maintain support for the institution. Instead of looking at the short term and making decisions day to day, justices are strategic in their planning and make decisions for the long term. 120
Other studies have revealed a more complex relationship between public opinion and judicial decisions, largely due to the difficulty of measuring where the effect can be seen. Some studies look at the number of reversals taken by the Supreme Court, which are decisions with which the Court overturns the decision of a lower court. In one study, the authors found that public opinion slightly affects cases accepted by the justices. 121 In a study looking at how often the justices voted liberally on a decision, a stronger effect of public opinion was revealed. 122
Whether the case or court is currently in the news may also matter. A study found that if the majority of Americans agree on a policy or issue before the court, the court’s decision is likely to agree with public opinion. 123 A second study determined that public opinion is more likely to affect ignored cases than heavily reported ones. 124 In these situations, the court was also more likely to rule with the majority opinion than against it. For example, in Town of Greece v. Galloway (2014), a majority of the justices decided that ceremonial prayer before a town meeting was not a violation of the Establishment Clause. 125 The fact that 78 percent of U.S. adults recently said religion is fairly to very important to their lives 126 and 61 percent supported prayer in school 127 may explain why public support for the Supreme Court did not fall after this decision. 128
Overall, however, it is clear that public opinion has a less powerful effect on the courts than on the other branches and on politicians. 129 Perhaps this is due to the lack of elections or justices’ lifetime tenure, or perhaps we have not determined the best way to measure the effects of public opinion on the Court.


6.9: WORSHIP
Perhaps the most frequent use of art as a means of connecting to viewers’ lives through the ages has been for religious purposes, often entailing the aspects of worship whereby a deity, person, or narrative is presented for the viewer to use in order to express their devotion, as an occasion of worship, or to contemplate its meaning. Among the most formalized types are cult statues images of deities, saints, or revered figures such as Varaha, the boar-headed avatar , or physical form, of the Hindu god Vishnu. Here, Varaha is rescuing the goddess Bhudevi by slaying the demon that had trapped her in the ocean. (Figure 6.15) Dangling in mid-air as she holds his tusk, Varaha returned Bhuvedi to her rightful place on earth.
Other examples include the enormous altarpieces that were a central focus in churches during the Middle Ages, Renaissance, and Baroque (seventeenth century) eras in Europe, altarpieces such as El Transparente in the Cathedral of Toledo, Spain. Its elaborate carvings and gilding interplay with natural sunlight that streams in from strategically placed openings in the wall and ceiling. (Figure 6.16) Such works are designed to be awe inspiring, presenting the viewer/believer with a spectacular visual expression of mysteries of the faith.


5.6: Correct use of Ohm’s Law
One of the most common mistakes made by beginning electronics students in their application of Ohm’s Laws is mixing the contexts of voltage, current, and resistance. In other words, a student might mistakenly use a value for I through one resistor and the value for E across a set of interconnected resistors, thinking that they’ll arrive at the resistance of that one resistor. Not so! Remember this important rule: The variables used in Ohm’s Law equations must be common to the same two points in the circuit under consideration. I cannot overemphasize this rule. This is especially important in series-parallel combination circuits where nearby components may have different values for both voltage drop and current.
When using Ohm’s Law to calculate a variable pertaining to a single component, be sure the voltage you’re referencing is solely across that single component and the current you’re referencing is solely through that single component and the resistance you’re referencing is solely for that single component. Likewise, when calculating a variable pertaining to a set of components in a circuit, be sure that the voltage, current, and resistance values are specific to that complete set of components only! A good way to remember this is to pay close attention to the two points terminating the component or set of components being analyzed, making sure that the voltage in question is across those two points, that the current in question is the electron flow from one of those points all the way to the other point, that the resistance in question is the equivalent of a single resistor between those two points, and that the power in question is the total power dissipated by all components between those two points.
The “table” method presented for both series and parallel circuits in this chapter is a good way to keep the context of Ohm’s Law correct for any kind of circuit configuration. In a table like the one shown below, you are only allowed to apply an Ohm’s Law equation for the values of a single vertical column at a time:
Deriving values horizontally across columns is allowable as per the principles of series and parallel circuits:
Not only does the “table” method simplify the management of all relevant quantities, it also facilitates cross-checking of answers by making it easy to solve for the original unknown variables through other methods, or by working backwards to solve for the initially given values from your solutions. For example, if you have just solved for all unknown voltages, currents, and resistances in a circuit, you can check your work by adding a row at the bottom for power calculations on each resistor, seeing whether or not all the individual power values add up to the total power. If not, then you must have made a mistake somewhere! While this technique of “cross-checking” your work is nothing new, using the table to arrange all the data for the cross-check(s) results in a minimum of confusion.
Review
- Apply Ohm’s Law to vertical columns in the table.
- Apply rules of series/parallel to horizontal rows in the table.
- Check your calculations by working “backwards” to try to arrive at originally given values (from your first calculated answers), or by solving for a quantity using more than one method (from different given values).


2.2: The Selection Process
- Be able to name and discuss the steps in the selection process.
Once you have developed your recruitment plan, recruited people, and now have plenty of people to choose from, you can begin the selection process. The selection process refers to the steps involved in choosing people who have the right qualifications to fill a current or future job opening. Usually, managers and supervisors will be ultimately responsible for the hiring of individuals, but the role of human resource management (HRM) is to define and guide managers in this process. Similar to the recruitment process discussed in Chapter 4 “Recruitment”, the selection process is expensive. The time for all involved in the hiring process to review résumés, weight the applications, and interview the best candidates takes away time (and costs money) that those individuals could spend on other activities. In addition, there are the costs of testing candidates and bringing them in from out of town for interviews. In fact, the US Department of Labor and Statistics estimates the combined direct and indirect cost of hiring someone new can reach upwards of $40,000 (Hamm, 2011). Because of the high cost, it is important to hire the right person from the beginning and ensure a fair selection process. For example, the Austin, Texas, fire department calculated it would cost $150,000 to reinterview candidates, after the interview questions were leaked to the public, giving some candidates possibly unfair advantages in the interview process 1 .
The selection process consists of five distinct aspects:
-
Criteria development.
All individuals involved in the hiring process should be properly trained on the steps for interviewing, including developing criteria, reviewing résumés, developing interview questions, and weighting the candidates.
The first aspect to selection is planning the interview process, which includes criteria development. Criteria development means determining which sources of information will be used and how those sources will be scored during the interview. The criteria should be related directly to the job analysis and the job specifications. This is discussed in Chapter 4 “Recruitment”. In fact, some aspects of the job analysis and job specifications may be the actual criteria. In addition to this, include things like personality or cultural fit, which would also be part of criteria development. This process usually involves discussing which skills, abilities, and personal characteristics are required to be successful at any given job. By developing the criteria before reviewing any résumés, the HR manager or manager can be sure he or she is being fair in selecting people to interview. Some organizations may need to develop an application or a biographical information sheet. Most of these are completed online and should include information about the candidate, education, and previous job experience.
- Application and résumé review. Once the criteria have been developed (step one), applications can be reviewed. People have different methods of going through this process, but there are also computer programs that can search for keywords in résumés and narrow down the number of résumés that must be looked at and reviewed.
- Interviewing. After the HR manager and/or manager have determined which applications meet the minimum criteria, he or she must select those people to be interviewed. Most people do not have time to review twenty or thirty candidates, so the field is sometimes narrowed even further with a phone interview. This is discussed in “Types of Interviews”.
- Test administration. Any number of tests may be administered before a hiring decision is made. These include drug tests, physical tests, personality tests, and cognitive tests. Some organizations also perform reference checks, credit report checks, and background checks. Types of tests are discussed in Section 5.4.1 “Testing”. Once the field of candidates has been narrowed down, tests can be administered.
- Making the offer. The last step in the selection process is to offer a position to the chosen candidate. Development of an offer via e-mail or letter is sometimes a more formal part of this process. Compensation and benefits will be defined in an offer. We discuss this in Chapter 6 “Compensation and Benefits”.
Fortune 500 Focus
In a 2010 interview (Bryant, 2010), Robert Selander, then CEO of MasterCard, cited presence as one of the most important aspects to acing an interview. He describes how, in any large organization, an employee will be expected to engage with a variety of stakeholders, from a member of Congress to a contractor replacing the carpet in the building. He says that a good employee—at any level of the organization—should be able to communicate well but also be able to communicate to a variety of stakeholders. We discuss communication in Chapter 9 “Successful Employee Communication”. Selander also says he will always ask the candidate about his or her weaknesses, but more importantly, how the candidate plans to address those weaknesses to make sure they do not become a barrier to success. He always asks the question “What can you do for us?” When asked if he could pose only one interview question, what would it be, his answer was, “Share with me two situations, work related that you are proud of, where something was achieved based on your own personal initiative and the other where the achievement was a result of the team getting something done that you could not have done alone.” In other words, Selander is looking for not only personal ability but the ability to work within a team to accomplish tasks. Selander offers advice to new college grads: try to find an organization where you can be involved and see all aspects of the business and be provided training to help you with certain skills that will be needed.
When was the last time you interviewed for a job? Did the process seem to flow smoothly? Why or why not?
- The selection process refers to the steps involved in choosing someone who has the right qualifications to fill a current or future job opening.
- There are five main steps in the selection process. First, criteria are developed to determine how the person will be chosen. Second is a review of the applications and résumés, often done via a computer program that can find keywords. Next is interviewing the employee. The last steps involve testing, such as a personality test or drug test, and then finally, making the offer to the right candidate.
- What components are included in the selection process? Which one do you think is the most important?
1 KVUE News, “Re-Interview Process to Cost $150,000,” June 23, 2011, accessed August 2, 2011, www.kvue.com/news/local/AFD–124452379.html.
References
Bryant, A., “The X Factor When Hiring? Call It Presence,” June 26, 2010, New York Times , accessed July 12, 2011, www.nytimes.com/2010/06/27/business/27corner.html?scp=1&sq=Selander&st=cse&pagewanted=1.
Hamm, L., “Pre-Employment Testing,” IHD Corporation, n.d., accessed August 2, 2011, www.ihdcorp.com/articles-hr/pre-employment-testing.htm.


12.7: Results and Employee Engagement
- Discuss the benefits of employee engagement
Employee Engagement
What is employee engagement? At its surface, employee engagement is a workplace methodology focused on fostering an inclusive and nurturing environment that motivates each employee to put forth their best effort every day. Employee engagement needs to be a team effort between the employee and the employer in order to be effective. Employees are responsible for their personal actions and attitudes; however, employers play a huge role in cultivating a pleasant and welcoming environment in the workplace. Employee engagement is not something that can be built overnight. Engagement is a continuous process that needs to be a conscious part of a company’s daily operations in order to yield effective results.
There are many components and nuances in employee engagement. From an employee standpoint, engagement can be broken down into two main factors: attitudes and actions.
Attitudes
The attitudes of employees include both their thoughts and their feelings. What does an employee think about their job? Do they understand their job functions and feel supported in their role? Do employees feel valued as a member of the team, or do they feel secluded and unsupported? It is impossible to precisely gauge employee attitudes; however, the way employees think and feel has a significant impact on the workplace and employee engagement. Employees who feel trusted and supported, and believe their job performance is valued, will perform better and exert more energy to go above and beyond.
Actions
An employee’s attitude directly correlates to their actions. If an employee has a poor attitude towards their company, their team, or their job, they are less likely to perform at expected levels. Disengaged employees are unmotivated and dissatisfied with their current job or job functions. They are more likely to show up late, leave work early, or put forth lackluster effort when completing their job functions. On the other hand, engaged employees are more likely to not only complete their job, but take extra steps to perform the job at the highest possible level. Employee actions directly impact their company’s profitability and reputation. Therefore, employee engagement also directly impacts a company’s bottom line and public perception.
Benefits of Employee Engagement
The benefits of employee engagement can manifest in a number of ways. One of the most obvious benefits of employee engagement is employee job satisfaction. If employees are more engaged, they are more satisfied with what they are doing and vice versa. Directly correlated to employee job satisfaction, is reduced turnover. People who are satisfied with their jobs are significantly less likely to search for another job than those that are unhappy. Reduced turnover helps companies save time and money by not having to spend as many resources on hiring and onboarding new employees.
Productivity is another large benefit of employee engagement. People who are engaged and satisfied with their jobs are more likely to show up to work each and every day. Disengaged employees on the other hand, are more likely to call out from work as they do not feel a strong sense of loyalty to their company. Employees with high attendance perform their job functions with higher productivity, since they spend more time at work. And, you guessed it, higher productivity leads to higher profitability for the company. Engaged employees are also more likely to have positive relationships with clients and customers. Positive relationships help to retain customers and can lead to an increase in customer referrals, all of which help to improve profitability.
You can also download a transcript for the video “What Great Employee Engagement Looks Like.”
Now that you have a better understanding of employee engagement, let’s move on to the next section to discuss ways in which employers and employees alike can drive engagement.
Sources
Robins, Alison. “ 6 Amazing Benefits Of Employee Engagement .” Officevibe, March 24, 2017.
“ What Is Employee Engagement .” Engage for Success. Accessed October 22, 2019.
Contributors and Attributions
- Results and Employee Engagement. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution
- Untitled. Authored by : Graphic Mama-team. Provided by : Pixabay. Located at : pixabay.com/illustrations/meeting-business-brainstorming-1453895/. License : CC0: No Rights Reserved . License Terms : Pixabay License
- Modification of Puzzles. Authored by : Gerd Altmann. Provided by : Pixabay. Located at : pixabay.com/photos/hand-keep-puzzle-finger-match-523231/. License : CC0: No Rights Reserved . License Terms : Pixabay License
- What Great Employee Engagement Looks Like. Authored by : BlessingWhite, a division of GP Strategies. Located at : https://youtu.be/VA_z5mvjeLc . License : All Rights Reserved . License Terms : Standard YouTube License


11.8E: Exercises
-
- Last updated
- Save as PDF
Practice Makes Perfect
Exercise \(\PageIndex{23}\) Graph Quadratic Functions of the Form \(f(x)=x^{2}=k\)
In the following exercises,
- Graph the quadratic functions on the same rectangular coordinate system
-
Describe what effect adding a constant, \(k\), to the function has on the basic parabola.
- \(f(x)=x^{2}, g(x)=x^{2}+4, \text { and } h(x)=x^{2}-4\)
- \(f(x)=x^{2}, g(x)=x^{2}+7, \text { and } h(x)=x^{2}-7\)
- Answer
-
1.
-
Figure 9.7.71 - The graph of \(g(x)=x^{2}+4\) is the same as the graph of \(f(x)=x^{2}\) but shifted up \(4\) units. The graph of \(h(x)=x^{2}-4\) is the same as the graph of \(f(x)=x^{2}\) but shift down \(4\) units.
-
Exercise \(\PageIndex{24}\) Graph Quadratic Functions of the Form \(f(x)=x^{2}=k\)
In the following exercises, graph each function using a vertical shift.
- \(f(x)=x^{2}+3\)
- \(f(x)=x^{2}-7\)
- \(g(x)=x^{2}+2\)
- \(g(x)=x^{2}+5\)
- \(h(x)=x^{2}-4\)
- \(h(x)=x^{2}-5\)
- Answer
-
1.
3.
5.
Exercise \(\PageIndex{25}\) Graph Quadratic Functions of the Form \(f(x)=(x-h)^{2}\)
In the following exercises,
- Graph the quadratic functions on the same rectangular coordinate system
-
Describe what effect adding a constant, \(h\), inside the parentheses has
- \(f(x)=x^{2}, g(x)=(x-3)^{2}, \text { and } h(x)=(x+3)^{2}\)
- \(f(x)=x^{2}, g(x)=(x+4)^{2}, \text { and } h(x)=(x-4)^{2}\)
- Answer
-
1.
-
Figure 9.7.75 - The graph of \(g(x)=(x−3)^{2}\) is the same as the graph of \(f(x)=x^{2}\) but shifted right \(3\) units. The graph of \(h(x)=(x+3)^{2}\) is the same as the graph of \(f(x)=x^{2}\) but shifted left \(3\) units.
-
Exercise \(\PageIndex{26}\) Graph Quadratic Functions of the Form \(f(x)=(x-h)^{2}\)
In the following exercises, graph each function using a horizontal shift.
- \(f(x)=(x-2)^{2}\)
- \(f(x)=(x-1)^{2}\)
- \(f(x)=(x+5)^{2}\)
- \(f(x)=(x+3)^{2}\)
- \(f(x)=(x-5)^{2}\)
- \(f(x)=(x+2)^{2}\)
- Answer
-
1.
3.
5.
Exercise \(\PageIndex{27}\) Graph Quadratic Functions of the Form \(f(x)=(x-h)^{2}\)
In the following exercises, graph each function using transformations.
- \(f(x)=(x+2)^{2}+1\)
- \(f(x)=(x+4)^{2}+2\)
- \(f(x)=(x-1)^{2}+5\)
- \(f(x)=(x-3)^{2}+4\)
- \(f(x)=(x+3)^{2}-1\)
- \(f(x)=(x+5)^{2}-2\)
- \(f(x)=(x-4)^{2}-3\)
- \(f(x)=(x-6)^{2}-2\)
- Answer
-
1.
3.
5.
7.
Exercise \(\PageIndex{28}\) Graph Quadratic Functions of the Form \(f(x)=ax^{2}\)
In the following exercises, graph each function.
- \(f(x)=-2 x^{2}\)
- \(f(x)=4 x^{2}\)
- \(f(x)=-4 x^{2}\)
- \(f(x)=-x^{2}\)
- \(f(x)=\frac{1}{2} x^{2}\)
- \(f(x)=\frac{1}{3} x^{2}\)
- \(f(x)=\frac{1}{4} x^{2}\)
- \(f(x)=-\frac{1}{2} x^{2}\)
- Answer
-
1.
3.
5.
7.
Exercise \(\PageIndex{29}\) Graph Quadratic Functions Using Transformations
In the following exercises, rewrite each function in the \(f(x)=a(x−h)^{2}+k\) form by completing the square.
- \(f(x)=-3 x^{2}-12 x-5\)
- \(f(x)=2 x^{2}-12 x+7\)
- \(f(x)=3 x^{2}+6 x-1\)
- \(f(x)=-4 x^{2}-16 x-9\)
- Answer
-
1. \(f(x)=-3(x+2)^{2}+7\)
3. \(f(x)=3(x+1)^{2}-4\)
Exercise \(\PageIndex{30}\) Graph Quadratic Functions Using Transformations
In the following exercises,
- Rewrite each function in \(f(x)=a(x−h)^{2}+k\) form
-
Graph it by using transformations
- \(f(x)=x^{2}+6 x+5\)
- \((x)=x^{2}+4 x-12\)
- \(f(x)=x^{2}+4 x-12\)
- \(f(x)=x^{2}-6 x+8\)
- \(f(x)=x^{2}-6 x+15\)
- \(f(x)=x^{2}+8 x+10\)
- \(f(x)=-x^{2}+8 x-16\)
- \(f(x)=-x^{2}+2 x-7\)
- \(f(x)=-x^{2}-4 x+2\)
- \(f(x)=-x^{2}+4 x-5\)
- \(f(x)=5 x^{2}-10 x+8\)
- \(f(x)=3 x^{2}+18 x+20\)
- \(f(x)=2 x^{2}-4 x+1\)
- \(f(x)=3 x^{2}-6 x-1\)
- \(f(x)=-2 x^{2}+8 x-10\)
- \(f(x)=-3 x^{2}+6 x+1\)
- Answer
-
1.
- f(x)=(x+3)^{2}-4
3.
- \(f(x)=(x+2)^{2}-1\)
5.
- \(f(x)=(x-3)^{2}+6\)
7.
- \(f(x)=-(x-4)^{2}+0\)
9.
- \(f(x)=-(x+2)^{2}+6\)
11.
- \(f(x)=5(x-1)^{2}+3\)
13.
- \(f(x)=2(x-1)^{2}-1\)
15.
- \(f(x)=-2(x-2)^{2}-2\)
Exercise \(\PageIndex{31}\) Graph Quadratic Functions Using Transformations
In the following exercises,
- Rewrite each function in \(f(x)=a(x−h)^{2}+k\) form
-
Graph it using properties
- \(f(x)=2 x^{2}+4 x+6\)
- \(f(x)=3 x^{2}-12 x+7\)
- \(f(x)=-x^{2}+2 x-4\)
- \(f(x)=-2 x^{2}-4 x-5\)
- Answer
-
1.
- \(f(x)=2(x+1)^{2}+4\)
3.
- \(f(x)=-(x-1)^{2}-3\)
Exercise \(\PageIndex{32}\) Matching
In the following exercises, match the graphs to one of the following functions:
- \(f(x)=x^{2}+4\)
- \(f(x)=x^{2}-4\)
- \(f(x)=(x+4)^{2}\)
- \(f(x)=(x-4)^{2}\)
- \(f(x)=(x+4)^{2}-4\)
- \(f(x)=(x+4)^{2}+4\)
- \(f(x)=(x-4)^{2}-4\)
-
\(f(x)=(x-4)^{2}+4\)
-
Figure 9.7.97 -
Figure 9.7.98 -
Figure 9.7.99 -
Figure 9.7.100 -
Figure 9.7.101 -
Figure 9.7.102 -
Figure 9.7.103 -
Figure 9.7.104
-
- Answer
-
1. c
3. e
5. d
7. g
Exercise \(\PageIndex{33}\) Find a Quadratic Function from its Graph
In the following exercises, write the quadratic function in \(f(x)=a(x−h)^{2}+k\) form whose graph is shown.
-
Figure 9.7.105 -
Figure 9.7.106 -
Figure 9.7.107 -
Figure 9.7.108
- Answer
-
1. \(f(x)=(x+1)^{2}-5\)
3. \(f(x)=2(x-1)^{2}-3\)
Exercise \(\PageIndex{34}\) Writing Exercise
- Graph the quadratic function \(f(x)=x^{2}+4x+5\) first using the properties as we did in the last section and then graph it using transformations. Which method do you prefer? Why?
- Graph the quadratic function \(f(x)=2x^{2}−4x−3\) first using the properties as we did in the last section and then graph it using transformations. Which method do you prefer? Why?
- Answer
-
1. Answers may vary.
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. After looking at the checklist, do you think you are well-prepared for the next section? Why or why not?


7.6: Geometry of Surfaces
If you've got a surface in your hand, you can find a homeomorphic version of the surface on which to construct hyperbolic geometry, elliptic geometry, or Euclidean geometry. And the choice of geometry is unique: No surface admits more than one of these geometries. As we shall see, of the infinitely many surfaces, all but four admit hyperbolic geometry (two admit Euclidean geometry and two admit elliptic geometry). Thus, if you randomly generate a constant curvature surface for a two-dimensional bug named Bormit, Bormit will no doubt live in a world with hyperbolic geometry.
Chances are, too, that a constant curvature surface cannot be embedded in three-dimensional space. Only the sphere has this nice feature. In fact, if \(X\) is any surface that lives in \(\mathbb{R}^3\text{,}\) like the handlebody surfaces in Figure \(7.5.6\), then it must have at least one point with positive curvature. Why is this? The surface in \(\mathbb{R}^3\) is bounded, so there must be some sphere in \(\mathbb{R}^3\) centered at the origin that contains the entire surface. Shrink this sphere until it just bumps into the surface at some point. The curvature of the surface at this point matches the curvature of the sphere, which is positive.
We have seen that any surface is homeomorphic to a polygonal surface representing \(H_g\) or \(C_g\text{,}\) for some \(g\text{,}\) and we now show that each of these may be given a homogeneous, isotropic and metric geometry (so that it has constant curvature). A polygonal surface can only run into trouble homogeneity-wise where the corners come together. Any point in the interior of the polygon has a nice \(360^\circ\) patch of space about it, as does any point in the interior of an edge. However, if the angles of the corners that come together at a point do not add up to \(360^{\circ}\text{,}\) then the surface has either a cone point or a saddle-point, depending on whether the angle sum is less than or more than \(360^{\circ}\text{.}\) As we saw in Chapter 1 (Exercises \(1.3.5\) and Example \(1.3.7\)), in either case, we will not have a homogeneous geometry; a two-dimensional bug would be able to distinguish (with triangles or circles) a cone point from a flat point from a saddle point.
To smooth out such cone points or saddle points we change the angles at the corners so that the angles do add up to \(360^\circ\text{.}\) We now have the means for doing this. If we need to shrink the corner angles, we can put the polygon in the hyperbolic plane. If we need to expand the angles, we can put the polygon in the projective plane.
The standard polygonal representation of \(C_3 = \mathbb{P}^2\# \mathbb{P}^2 \# \mathbb{P}^2\text{,}\) is a hexagon having boundary label \(a_1a_1a_2a_2a_3a_3\text{,}\) as in Figure \(7.6.1\). All six corners of the hexagon come together at a single point. In the Euclidean plane, a regular hexagon has corner angles equal to \(120^{\circ}\text{.}\) To avoid a saddle point when joining the six corners together, shrink the corner angles to \(60^{\circ}\text{.}\) A tiny copy of a regular hexagon in the hyperbolic plane will have corner angles just under \(120^{\circ}\text{.}\) If the hexagon grows so that its vertices approach ideal points, its corner angles will approach \(0^{\circ}\text{.}\) At some point, then, the interior angles will be \(60^{\circ}\) on the nose. (We may construct this precise hexagon as well. See Exercise \(7.6.4\).) If \(C_3\) is built from this hexagon living in the hyperbolic plane, the surface inherits the geometry of the space in which it finds itself; that is, the surface \(C_3\) admits hyperbolic geometry, a nice homogeneous, isotropic and metric geometry.
Revisiting Example \(1.3.4\), consider the hexagon with boundary label \(abcabc\text{.}\) The six corners of this polygonal surface come together in groups of two. These corners create cone points because the angle sum of the two corners coming together is less than \(360^{\circ}\) in the Euclidean plane. We can avoid cone points by putting the hexagon in \(\mathbb{P}^2\text{.}\) A small regular hexagon in the projective plane will have corner angles just slightly greater than \(120^{\circ}\text{,}\) but we need each corner angle to expand to \(180^{\circ}\text{.}\) We may achieve these angles by expanding the hexagon until it covers the entire projective plane. In fact, the surface of Example \(1.3.4\) is the projective plane, and it admits elliptic geometry.
Each surface admits one homogeneous, isotropic, and metric geometry. In particular, the sphere (\(H_0\)) and projective plane (\(C_1\)) admit elliptic geometry. The torus (\(H_1\)) and Klein bottle (\(C_2\)) admit Euclidean geometry. All handlebody surfaces \(H_g\) with \(g \geq 2\) and all cross-cap surfaces \(C_g\) with \(g \geq 3\) admit hyperbolic geometry.
The following section offers a more formal discussion of how any surface admits one of our three geometries but we present an intuitive argument here.
The sphere and projective plane admit elliptic geometry by construction: The space in elliptic geometry is the projective plane, and via stereographic projection, this is the geometry on \(\mathbb{S}^2\text{.}\)
The torus and Klein bottle are built from regular \(4\)-gons (squares) whose edges are identified in such a way that all \(4\) corners come together at a point. In each case, if we place the square in the Euclidean plane all corner angles are \(\dfrac{\pi}{2}\text{,}\) so the sum of the angles is \(2\pi\text{,}\) and our surfaces admit Euclidean geometry.
Each handlebody surfaces \(H_g\) for \(g \geq 2\) and each cross-cap surfaces \(C_g\) for \(g \geq 3\) can be built from a regular \(n\)-gon where \(n \geq 6\text{.}\) Again, all \(n\) corners come together at a single point. A regular \(n\)-gon in the Euclidean plane has interior angle \(\dfrac{(n-2)\pi}{n}\) radians, so the corner angles sum to \((n-2)\pi\) radians. This angle sum exceeds \(2\pi\) radians since \(n \geq 6\text{.}\) Placing a small version of this \(n\)-gon in the hyperbolic plane, the corner angle sum will be very nearly equal to \((n-2)\pi\) radians and will exceed \(2\pi\) radians, but as we expand the \(n\)-gon the corners approach ideal points and the corner angles sum will approach \(0\) radians. Thus, at some point the angle sum will equal \(2\pi\) radians on the nose, and the polygonal surface built from this precise \(n\)-gon admits hyperbolic geometry. Exercise \(7.6.4\) works through how to construct this precise \(n\)-gon.
Of course, one need not build a surface from a regular polygon. For instance, the torus can be built from any rectangle in the Euclidean plane and it will inherit Euclidean geometry. So while the type of geometry our surface admits is determined, we have some flexibility where certain geometric measurements are concerned. For instance, there is no restriction on the total area of the torus, and the rectangle on which it is formed can have arbitrary length and width dimensions. These dimensions would have a simple, tangible meaning to a two-dimensional bug living in the surface (and might be experimentally determined). Each dimension corresponds to the length of a geodesic path that would return the bug to its starting point. A closed geodesic path in a surface is a path that follows along a straight line (in the underlying geometry) that starts and ends at the same point. Figure \(7.6.2\) shows three closed geodesic paths, all starting and ending at a point near a bug's house. The length of one path equals the width of the rectangle, the length of another equals the length of the rectangle, and the third follows a path that is longer than the first two.
Even in hyperbolic surfaces, where the area of the surface is fixed (for a given curvature) by the Gauss-Bonnet formula, which we prove shortly, there is freedom in determining the length of closed geodesic paths.
If we make three slices in the two-holed torus we obtain two pairs of pants, as indicated in the following figure.
We label our cuts so that we can stitch up our surface later. Match the \(c_i\text{,}\) \(d_i\text{,}\) and \(e_i\) edges to recover the two-holed torus. Any pair of pants can be cut into two hexagons by cutting along the three vertical seams in the pants. It follows that the two-holed torus can be constructed from four hexagons, with edges identified in pairs as indicated below.
The four hexagons represent a cell division of \(H_2\) having \(6\) vertices, \(12\) edges, and \(4\) faces. In the edge identification, corners come together in groups of \(4\), so we need each corner angle to equal \(90^\circ\) in order to endow it with a homogeneous geometry. We know we can do this in the hyperbolic plane. Moreover, according to Theorem \(5.4.6\), there is freedom in choosing the dimensions of the hexagons. That is, for each triple of real numbers \((a,b,c)\) there exists a right-angled hexagon in \(\mathbb{D}\) with alternate lengths \(a,b,\) and \(c\text{.}\) So, there exists a two-holed torus for each combination of six seam lengths (\(a_1,a_2,a_3,b_1,b_2,\) and \(b_3\)).
A surface that admits one of our three geometries will have constant curvature. The reader might have already noticed that the sign of the curvature will equal the sign of the surface's Euler characteristic. Of course the magnitude of the curvature (if \(k \neq 0)\) can vary if we place a polygonal surface in a scaled version of \(\mathbb{P}^2\) or \(\mathbb{D}\text{.}\) That is, while the type of homogeneous geometry a surface admits is determined by its Euler characteristic (which is determined by its shape), the curvature scale can vary if \(k \neq 0\text{.}\) By changing the radius of a sphere, we change its curvature (though it always remains positive). Similarly, the surface \(C_3\) in Figure \(7.6.1\) has constant curvature \(-1\) if it is placed in the hyperbolic plane of Chapter 5. However, it can just as easily find itself in the hyperbolic plane with curvature \(k = -8\text{.}\) Recall, the hyperbolic plane with curvature \(k \lt 0\) is modeled on the open disk in \(\mathbb{C}\) centered at the origin with radius \(\dfrac{1}{\sqrt{|k|}}\text{.}\) Placing the hexagonal representation of \(C_3\) into this space so that its corner angle sum is still \(2\pi\) produces a surface with constant curvature \(k\text{.}\)
We have finally arrived at the elegant relationship between a surface's curvature \(k\text{,}\) its area, and its Euler characteristic. This relationship crystalizes the interaction between the topology and geometry of surfaces.
The area of a surface with constant curvature \(k\) and Euler characteristic \(\chi\) is given by the formula \(kA = 2\pi \chi.\)
- Proof
-
The sphere with constant curvature \(k\) has radius equal to \(\dfrac{1}{\sqrt{k}}\text{,}\) and area equal to \(\dfrac{4\pi}{k}\text{.}\) Since the sphere has Euler characteristic \(2\), the Gauss-Bonnet formula holds in this case. The projective plane \(\mathbb{P}^2\) with curvature \(k\) has area equal to \(\dfrac{2\pi}{k}\text{,}\) and Euler characteristic equal to \(1\), so the result holds in this case as well. The torus and the Klein bottle each have \(k = 0\) and \(\chi = 0\text{,}\) so in this case the Gauss-Bonnet formula reduces to the true statement that \(0 = 0\text{.}\)
Any surface of constant negative curvature cam be represented by a regular \(n\)-sided polygon with \(n \geq 6\text{.}\) Furthermore, this polygon can be placed in the hyperbolic plane with curvature \(k \lt 0\text{,}\) so that its interior angles sum to \(2\pi\) radians. According to Theorem \(7.4.3\),
\[ kA = 2\pi - (n-2)\pi = 2\pi\bigg(2-\dfrac{n}{2}\bigg)\text{,} \]
where \(A\) is the area of the \(n\)-gon.
Now, for \(g \geq 2\text{,}\) \(H_g\) is represented by a \(4g\)-gon so that
\[ kA = 2\pi(2-2g)=2\pi\chi(H_g)\text{.} \]
For \(g \geq 3\text{,}\) \(C_g\) is represented by a \(2g\)-gon so that
\[ kA=2\pi(2-g) = 2\pi\chi(C_g)\text{.} \]
This completes the proof.
Suppose a two-dimensional cosmologist believes she lives in a surface of constant curvature (because her universe looks homogeneous and isotropic). If she can deduce the curvature of the universe and its total area, she will know its Euler characteristic. That is, by measuring these geometric properties she can deduce the shape of her universe, or, at worst, narrow down the possibilities to two. If \(\chi\) is \(2\) or an odd integer then the cosmologist will know the shape of the universe. If \(\chi \lt 2\) is even, her universe will have one of two possible shapes - one shape orientable, the other non-orientable.
Exercises
Suppose our intrepid team of two-dimensional explorers from Exercise \(7.4.4\), after an extensive survey, estimates with high confidence that the area of their universe is between \(800,000\) km\(^2\) and \(900,000\) km\(^2\text{.}\) Assuming their universe is homogeneous and isotropic, what shapes are possible for their universe? Can they deduce from this information the orientability status of their universe?
Suppose a certain constant curvature \(3\)-holed torus \(H_3\) has area \(5.2\) km\(^2\text{.}\) What must be the area of a constant curvature \(C_3\) surface so that they have the same curvature?
Building a hyperbolic surface from pairs of pants. To construct \(H_g\) for \(g \geq 2\) from pairs of pants, how many do we need? Express your answer in terms of \(g\text{.}\)
Suppose we want to build a regular \(n\)-gon in \((\mathbb{D},{\cal H})\) from the vertices \(v_k = r e^{i \frac{k}{n}2\pi}\) for \(k=0,1,\ldots,n-1\) so that the \(n\) interior angles sum to \(2 \pi\text{.}\) Prove that this is the case when \(r = \sqrt{\cos(\dfrac{2\pi}{n})}\text{.}\)
- Hint
-
It may be helpful to refer to Exercise \(5.4.9\) where we proved this result in the case \(n=8\text{.}\)


4.1: Lewis structures
8
Harper College Chemistry Department
Summary
By the end of this section, you will be able to:
- Write Lewis symbols for neutral atoms and ions
- Draw Lewis structures depicting the bonding in simple molecules
We have discussed the various types of bonds that form between atoms. These bonds involve the sharing or transfer of valence shell electrons between atoms. In this section, we will explore the typical method for depicting valence shell electrons and chemical bonds, namely Lewis symbols and Lewis structures.
Lewis Symbols
We use Lewis symbols to describe valence electron configurations of atoms and monatomic ions. A Lewis symbol consists of an elemental symbol surrounded by one dot for each of its valence electrons:
Figure 1 shows the Lewis symbols for the elements of the third period of the periodic table.
Lewis symbols can also be used to illustrate the formation of cations from atoms, as shown here for sodium and calcium:
Likewise, they can be used to show the formation of anions from atoms, as shown here for chlorine and sulfur:
Figure 2 demonstrates the use of Lewis symbols to show the transfer of electrons during the formation of ionic compounds.
Lewis Structures
We also use Lewis symbols to indicate the formation of covalent bonds, which are shown in Lewis structures, drawings that describe the bonding in molecules and polyatomic ions. For example, when two chlorine atoms form a chlorine molecule, they share one pair of electrons:
The Lewis structure indicates that each Cl atom has three pairs of electrons that are not used in bonding (called lone pairs) and one shared pair of electrons (written between the atoms). A dash (or line) is sometimes used to indicate a shared pair of electrons:
A single shared pair of electrons is called a single bond. Each Cl atom interacts with eight valence electrons: the six in the lone pairs and the two in the single bond.
The Octet Rule
The other halogen molecules (F 2 , Br 2 , I 2 and At 2 ) form bonds like those in the chlorine molecule: one single bond between atoms and three lone pairs of electrons per atom. This allows each halogen atom to have a noble gas electron configuration. The tendency of main group atoms to form enough bonds to obtain eight valence electrons is known as the octet rule.
The number of bonds that an atom can form can often be predicted from the number of electrons needed to reach an octet (eight valence electrons); this is especially true of the nonmetals of the second period of the periodic table (C, N, O, and F). For example, each atom of a group 14 element has four electrons in its outermost shell and therefore requires four more electrons to reach an octet. These four electrons can be gained by forming four covalent bonds, as illustrated here for carbon in CCl 4 (carbon tetrachloride) and silicon in SiH 4 (silane). Because hydrogen only needs two electrons to fill its valence shell, it is an exception to the octet rule. The transition elements and inner transition elements also do not follow the octet rule:
Group 15 elements such as nitrogen have five valence electrons in the atomic Lewis symbol: one lone pair and three unpaired electrons. To obtain an octet, these atoms form three covalent bonds, as in NH 3 (ammonia). Oxygen and other atoms in group 16 obtain an octet by forming two covalent bonds:
Double and Triple Bonds
As previously mentioned, when a pair of atoms shares one pair of electrons, we call this a single bond. However, a pair of atoms may need to share more than one pair of electrons in order to achieve the requisite octet. A double bond forms when two pairs of electrons are shared between a pair of atoms, as between the carbon and oxygen atoms in CH 2 O (formaldehyde) and between the two carbon atoms in C 2 H 4 (ethylene):
A triple bond forms when three electron pairs are shared by a pair of atoms, as in carbon monoxide (CO) and the cyanide ion (CN – ):
Writing Lewis Structures with the Octet Rule
For very simple molecules and molecular ions, we can write the Lewis structures by merely pairing up the unpaired electrons on the constituent atoms. See these examples:
For more complicated molecules and molecular ions, it is helpful to follow the step-by-step procedure outlined here:
- Determine the total number of valence (outer shell) electrons. For cations, subtract one electron for each positive charge. For anions, add one electron for each negative charge.
- Draw a skeleton structure of the molecule or ion, arranging the atoms around a central atom. (Generally, the least electronegative element should be placed in the center.) Connect each atom to the central atom with a single bond (one electron pair).
- Distribute the remaining electrons as lone pairs on the terminal atoms (except hydrogen), completing an octet around each atom; following the octet rule.
- Place all remaining electrons on the central atom.
- Rearrange the electrons of the outer atoms to make multiple bonds with the central atom in order to obtain octets wherever possible.
-
Determine the total number of valence (outer shell) electrons in the molecule or ion.For a molecule, we add the number of valence electrons (VE) on each atom in the molecule:
SiH 4 (Si: 4 VE/atom × 1 atom=4 VE) + (H: 1 VE/atom × 4 atoms=4 VE) = 8 VE
For a negative ion , such as CHO 2 − , we add the number of valence electrons on the atoms to the number of negative charges on the ion (one electron is gained for each single negative charge):
CHO 2 − (C: 4 VE/atom × 1 atom=4 VE) + (H: 1 VE/atom × 1 atom=1 VE) +
(O: 6 VE/atom × 2 atoms=12 VE) + (1 additional electron=1 VE) = 18 VEFor a positive ion , such as NO + , we add the number of valence electrons on the atoms in the ion and then subtract the number of positive charges on the ion (one electron is lost for each single positive charge) from the total number of valence electrons:
NO + (N: 5 VE/atom × 1 atom=5 VE) + (O: 6 VE/atom × 1 atom=6 VE) −
1 electron (positive charge)=10 VESince OF 2 is a neutral molecule, we simply add the number of valence electrons:
OF 2 (O: 6 VE/atom × 1 atom=6 VE) + (F: 7 VE/atom × 2 atoms=14 VE)=20 VE
- When several arrangements of atoms are possible, as for CHO 2 − , the less electronegative carbon atom occupies the central position with the oxygen and hydrogen atoms surrounding it. Other examples include P in POCl 3 , S in SO 2 , and Cl in ClO 4 − .
-
Distribute the remaining electrons as lone pairs on the terminal atoms (except hydrogen) to complete their valence shells with an octet of electrons.
There are no remaining electrons on SiH 4 , so it is unchanged:
-
Place all remaining electrons on the central atom.
For SiH 4 , CHO 2 − , and NO + , there are no remaining electrons; we already placed all of the electrons determined in Step 1.
For OF 2 , we had 16 electrons remaining in Step 3, and we placed 12, leaving 4 to be placed on the central atom:
-
Rearrange the electrons of the outer atoms to make multiple bonds with the central atom in order to obtain octets wherever possible.
SiH 4 : Si already has an octet, so nothing needs to be done.
CHO 2 − : We have distributed the valence electrons as lone pairs on the oxygen atoms,
but the carbon atom lacks an octet:
NO + : For this ion, we added eight valence electrons, but neither atom has an octet. We cannot add any more electrons since we have already used the total that we found in
Step 1, so we must move electrons to form a multiple bond:
This still does not produce an octet, so we must move another pair, forming a triple bond:
In OF 2 , each atom has an octet as drawn, so nothing changes.
Writing Lewis Structures: NASA’s Cassini-Huygens mission detected a large cloud of toxic hydrogen cyanide (HCN) on Titan, one of Saturn’s moons. Titan also contains ethane (H 3 CCH 3 ), acetylene (HCCH), and ammonia (NH 3 ). What are the Lewis structures of these molecules?
Solution
-
Calculate the number of valence electrons.
HCN: (1
×
1) + (4
×
1) + (5
×
1) = 10
H 3 CCH 3 : (1 × 3) + (2 × 4) + (1 × 3) = 14
HCCH: (1 × 1) + (2 × 4) + (1 × 1) = 10
NH 3 : (5 × 1) + (3 × 1) = 8
-
Draw a skeleton and connect the atoms with single bonds.
Remember that H is never a central atom: -
HCN: six electrons placed on N
H 3 CCH 3 : no electrons remain
HCCH: no terminal atoms capable of accepting electrons
NH 3 : no terminal atoms capable of accepting electrons
-
Where needed, place remaining electrons on the central atom:
HCN: no electrons remainH 3 CCH 3 : no electrons remain
HCCH: four electrons placed on carbon
NH 3 : two electrons placed on nitrogen
-
Where needed, rearrange electrons to form multiple bonds in order to obtain an octet on each atom:
HCN: form two more C–N bondsH 3 CCH 3 : all atoms have the correct number of electronsHCCH: form a triple bond between the two carbon atoms
NH 3 : all atoms have the correct number of electrons
Check Your Learning: Both carbon monoxide, CO, and carbon dioxide, CO 2 , are products of the combustion of fossil fuels. Both of these gases also cause problems: CO is toxic and CO 2 has been implicated in global climate change. What are the Lewis structures of these two molecules?
In case you are wondering
Key Concepts and Summary
Valence electronic structures can be visualized by drawing Lewis symbols (for atoms and monatomic ions) and Lewis structures (for molecules and polyatomic ions). Lone pairs, unpaired electrons and single, double or triple bonds are used to indicate where the valence electrons are located around each atom in a Lewis structure. Most structures—especially those containing second row elements—obey the octet rule, in which every atom (except H) is surrounded by eight electrons. Exceptions to the octet rule occur for odd-electron molecules (free radicals), electron-deficient molecules and hypervalent molecules.
Chemistry End of Chapter Exercises
1. Write the Lewis symbols for each of the following ions:
(a) As 3–
(b) I –
(c) Be 2+
(d) O 2–
(e) Ga 3+
(f) Li +
(g) N 3–
2. Many monatomic ions are found in seawater, including the ions formed from the following list of elements. Write the Lewis symbols for the monatomic ions formed from the following elements:
(a) Cl
(b) Na
(c) Mg
(d) Ca
(e) K
(f) Br
(g) Sr
(h) F
3. Write the Lewis symbols of the ions in each of the following ionic compounds and the Lewis symbols of the atom from which they are formed:
(a) MgS
(b) Al 2 O 3
(c) GaCl 3
(d) K 2 O
(e) Li 3 N
(f) KF
5. Write the Lewis structure for the diatomic molecule P 2 , an unstable form of phosphorus found in high-temperature phosphorus vapor.
6. Write Lewis structures for the following:
(a) H 2
(b) HBr
(c) PCl 3
(d) SF 2
(e) H 2 CCH 2
(f) HNNH
(g) H 2 CNH
(h) NO –
(i) N 2
(j) CO
(k) CN –
7. Write Lewis structures for the following:
(a) O 2
(b) H 2 CO
(c) AsF 3
(d) ClNO
(e) SiCl 4
(f) H 3 O +
(g) NH 4 +
(h) BF 4 –
(i) HCCH
(j) ClCN
(k) C 2 2-
8. Write Lewis structures for the following:
(a) ClF 3
(b) PCl 5
(c) BF 3
(d) PF 6 –
13. Methanol, H 3 COH, is used as the fuel in some race cars. Ethanol, C 2 H 5 OH, is used extensively as motor fuel in Brazil. Both methanol and ethanol produce CO 2 and H 2 O when they burn. Write the chemical equations for these combustion reactions using Lewis structures instead of chemical formulas.
14. Many planets in our solar system contain organic chemicals including methane (CH 4 ) and traces of ethylene (C 2 H 4 ), ethane (C 2 H 6 ), propyne (H 3 CCCH), and diacetylene (HCCCCH). Write the Lewis structures for each of these molecules.
15. Carbon tetrachloride was formerly used in fire extinguishers for electrical fires. It is no longer used for this purpose because of the formation of the toxic gas phosgene, Cl 2 CO. Write the Lewis structures for carbon tetrachloride and phosgene.
17. The arrangement of atoms in several biologically important molecules is given here. Complete the Lewis structures of these molecules by adding multiple bonds and lone pairs. Do not add any more atoms.
(a) the amino acid serine:
(b) urea:
(c) pyruvic acid:
(d) uracil:
(e) carbonic acid:
21. How are single, double, and triple bonds similar? How do they differ?
Glossary
- double bond
- covalent bond in which two pairs of electrons are shared between two atoms
- free radical
- molecule that contains an odd number of electrons
- hypervalent molecule
- molecule containing at least one main group element that has more than eight electrons in its valence shell
- Lewis structure
- diagram showing lone pairs and bonding pairs of electrons in a molecule or an ion
- Lewis symbol
- symbol for an element or monatomic ion that uses a dot to represent each valence electron in the element or ion
- lone pair
- two (a pair of) valence electrons that are not used to form a covalent bond
- octet rule
- guideline that states main group atoms will form structures in which eight valence electrons interact with each nucleus, counting bonding electrons as interacting with both atoms connected by the bond
- single bond
- bond in which a single pair of electrons is shared between two atoms
- triple bond
- bond in which three pairs of electrons are shared between two atoms


4.3: Emotional Development in Infants and Toddlers
-
- Last updated
- Save as PDF
Learning Objectives
By the end of this section, you will be able to:
- Discuss the relationship between emotion , mood, and emotion regulation
- Distinguish between primary and secondary emotions
- Identify the important early milestones in emotion regulation
Kylie has been close to her nephew Jack since he was a newborn. In his infancy, Jack seemed to express only a few emotions, by either crying or smiling. By his first birthday, when he could play with his toys or feed himself, he clearly showed happiness over his skills. He also showed signs of sadness and distress when he was tired or overwhelmed. When Jack was two years old, Kylie noticed that he started to demonstrate other emotions, like shyness around new people and pride when he dressed himself.
As Jack’s emotions became more complex, he also developed the ability to cope with and control them. At first, he was limited to looking away, turning his head, or sucking his pacifier. Later, Kylie would watch him rub his blankets or his hair to calm down. As he grew, Jack started to display typical toddler behaviors such as tantrums, which included wiggling, screaming, and running away to express himself.
At each stage in his development, Kylie needed to shift her approach to help support Jack with his emotions, sometimes giving him comfort, and sometimes giving him space and time. Luckily, she also learned how to anticipate and predict his emotions, noting his cues when he was tired or overstimulated, or when he was becoming frustrated and angry. Understanding infant emotions can help caregivers provide sensitive and responsive care that can ensure a supportive home environment. This section discusses the development of emotions during the first few years of life and the emergence of the ability to regulate and identify emotions.
Life Hacks: Understanding Temper Tantrums
Ever hear of the terrible twos? The “terrible twos” is a term used in some countries to describe the increased independence and tantrums sometimes seen in toddlers. While toddlers are learning to say “no” and struggling with emotions, these tantrums can be quite manageable for those with a bit of lifespan development knowledge. Toddlers often become frustrated if they are overstimulated or tired, so those late afternoon outbursts may be a sign that they need some quiet time or a nap. Sometimes a snack can help too. Because they are still learning to communicate, toddlers can often feel misunderstood, so paying attention to their body language, especially any pointing or grunting, can help you anticipate their needs and prevent a misunderstanding. A good routine and promoting goodness of fit may even prevent many tantrums from ever happening. For example, prioritizing a regular bedtime for a toddler over a late-night social occasion may avoid a grumpy morning.
Toddlers are often seeking autonomy , or control over themselves, and tantrums can erupt when they feel forced to go to bed, get into the car, or eat their food when they have other priorities. Giving a toddler a sense of choice, even if it’s a false choice, can help them feel better. For instance, if a toddler resists getting dressed, you can ask if they’d like to put on their left or right sock first. This opportunity for choice gives toddlers a sense of autonomy so they are less likely to have a tantrum. Allowing them to try to do things for themselves, like feeding, dressing, and tidying toys, can also help give toddlers a sense of autonomy that can alleviate a tantrum. You could even let them leave the house in those clothes that don’t match if they seem proud of their fashion choice.
When a temper tantrum occurs (and they will), stay calm. Some toddlers prefer to cuddle to help calm them, but others don’t want to be touched because they already feel overstimulated. Make sure they are physically safe and not near any hazards. Give them time to cry and release their emotions. If they are crying because they want something they should not have, don’t reward them by letting them have it; instead, find another reward to give them once they are calm. Most important, try not to scream or get agitated yourself. This response will only escalate emotions and make the tantrum last longer.
Emotions
An emotion is the temporary affective state or feelings that influence our physiology, facial expressions, and motivations. In the first month of life, infants tend to show two emotional states: pleasure and displeasure (Watson & Tellegen, 1985). These two states differ by whether an infant is looking away or toward, is reaching or avoiding, and is calm or in distress (sometimes referred to as approach or withdrawal). By the end of the first year of life, infants can typically express a variety of emotions such as joy, sadness, anger, and fear. An infant may have a relatively stable and calm temperament or mood, but they can still experience a variety of emotions in a short window of time.
Mood and Arousal
It can be a challenge to distinguish between an infant’s moods and emotions when both involve our affect , or underlying feelings. Our moods are long-lasting dispositions that describe our level of arousal and pleasure (Figure 4.8). Like the temperamental dimensions of affect and intensity, moods describe an infant’s typical level of arousal and pleasure along two continuous spectrums (Hay, 2019; Yik et al., 1999). An infant who is experiencing a high level of arousal and a high level of pleasure might be described as in an excited mood, whereas an infant with low arousal and low pleasure might be lethargic in mood. An infinite number of points along both these dimensions can describe infant mood.
In the first weeks after birth, infants’ levels of arousal can also be described as various states of consciousness. Pediatrician Berry Brazelton identified six discrete states of infant arousal ranging from deep sleep to active alert (Brazelton, 1973). Initially, these six states help describe an infant as sleeping soundly or lightly, awake but drowsy, alert, or very active. Over the course of the first year, new emotional states gradually start to emerge that are different from Brazelton’s six stages. The first is a heightened sense of pleasure or joy that emerges around three to five months of age, and the second is a more potent sense of distress or displeasure, apparent around six to eight months of age (Hay, 2019).
Primary Emotions
Although adults can experience more than 220 unique emotions, Paul Ekman (1992, 1999) identified six primary emotions , biologically based feelings that appear early in the first year of life and are associated with distinct and universal facial expressions (Table 4.2). That is, people across cultures can recognize the facial expressions of primary emotions. These primary emotions are found in nearly all human cultures and are also displayed by individuals who are blind from birth, suggesting they are biologically innate. In other words, across cultures and individual differences, many individuals show these same facial expressions corresponding to each of the six primary emotions. Another theorist, Carroll Izard (1977, 1991), initially identified ten primary emotions that appear early in infancy, and Robert Levenson identified emotions that have evolutionary adaptive features (Mauss et al., 2005). Although each of these theories is unique, they have considerable overlap and agree on the existence of six primary emotions: joy, sadness, fear, anger, disgust, and surprise (Tracy & Randles, 2011).
| Emotion | Facial Expression |
|---|---|
| Joy | Individual smiles, raises cheekbones, creases corners of the eyes |
| Sadness | Individual frowns, raises inner eyebrows, and may show tears |
| Fear | Individual widens eyes and stretches corners of the mouth |
| Anger | Individual moves eyebrows and corners of the mouth downward |
| Disgust | Individual crinkles nose, closes eyes, and may stick out tongue |
| Surprise | Individual widens eyes and opens mouth wide |
Link to Learning
Review this short video about how theories of early emotions gave us our current idea of primary emotions to learn more.
Secondary Emotions
Primary emotions can help infants communicate their needs, but there is a limit to how much they can express. Starting around eighteen months, secondary emotions begin to emerge (Lewis & Sullivan, 2005). Complex and specific to the situation, secondary emotions require infants to have a sense of self and therefore know who they are as opposed to who others are. Secondary emotions include emotions such as pride, embarrassment, jealousy, and empathy.
Secondary emotions in which a toddler becomes aware of how others view them are called self-conscious emotions . A toddler who believes they are viewed positively by others may feel emotions such as pride and confidence. If aware they are viewed negatively by others, they may feel emotions such as guilt, shame, or embarrassment.
Secondary emotions can also correspond to the way infants perceive others (Trevarthen, 2005). With these other-evaluative emotion s, or relational emotions, infants can judge others positively, such as with love and empathy (Lewis et al., 1989; Park & Lewis, 2021). Other-evaluative emotions that judge others negatively include jealousy and envy.
Emotion Regulation
Emotions are powerful and can be overwhelming. In infancy, regulating emotions is a difficult task because infants are limited in their coping strategies (Thomas et al., 2017). The ability to calm ourselves and move from a state of high arousal to a state of lower arousal is called emotion regulation . Infants are often dependent on their caregiver to help them calm down, with the caregiver and child forming a dyad, or a pair of individuals who influence one another. A good means for doing so is a process called dyadic regulation , in which a caregiver calmly holds, cuddles, and touches an infant to help them slow their breathing and heart rate (Figure 4.9) Dyadic regulation can also make use of distraction, such as rocking, feeding, bathing, or singing to an infant (Atkinson et al., 2021).
Dyadic regulation and emotion regulation are also supported by synchrony , or when caregivers and children are responding to each other’s emotions in reciprocal and sensitive ways (Feldman. 2007; Kerr et al., 2021). For example, when a father and infant smile or giggle while making eye contact, they are demonstrating good synchrony. When caregivers demonstrate sensitivity and responsiveness to their infant’s emotions, it can lower infant negative emotions and improve infant regulation (Abney et al., 2021; Gartstein et al., 2018). Understanding regulation strategies, the role of culture in emotion regulation, and emotional awareness will help you in your encounters, both personal and professional, with young children.
Regulation Strategies
A newborn who is overwhelmed and overstimulated may develop the regulation strategy of attentional distraction , such as by turning their head away and closing their eyes (Atkinson et al., 2021). As infants grow and can move and crawl, they can begin to use attentional distraction to move away from upsetting situations such as loud appliances in the home and toward calming situations, such as interesting toys.
When infants and toddlers are distressed and upset, self-soothing skills such as sucking that directly target the level of arousal can help regulate their heart rate and breathing (Atkinson et al., 2021).  Another self-soothing technique is touching and rubbing blankets, soft toys, or hair to calm down.
By the second year of life, young toddlers also engage in attention-seeking behaviors to help regulate themselves. These behaviors include crying and calling out for a caregiver, reaching and turning toward an adult, and wanting to be held or cuddled (Atkinson et al., 2021). Finally, near twenty-four months of age, escape behavior begins to emerge, in which toddlers attempt to hide, protest, avoid, and rebuke activities or experiences that bring them distress. An overtired or upset toddler may hide their face and curl on the floor, run to a corner, or throw items away to exit the activity they find upsetting. By being aware of an infant’s age, resources, and tools for emotion regulation, caregivers can begin helping them develop self-regulation skills over the first few years of life.
Supporting young infants and toddlers with emotion regulation skills has long-term benefits. Parents and caregivers who more often hold and cuddle their infants and respond to them with close soothing tend to more effectively promote infant development and soothability (Kiel et al., 2024). Moreover, caregivers who are sensitive to infants’ and toddlers’ nonverbal cues such as attentional distraction, attention-seeking, and escape behaviors can anticipate their emotional needs and prevent emotions from escalating into distress (Abney et al., 2021; Thomas et al., 2017). Finally, parents and caregivers who provide a supportive routine with adequate sleep and quiet time, regular feeding, and opportunities to move and wiggle can help toddlers to be well-rested and fed, which can help with the development of independent self-soothing behaviors (Kim et al., 2014).
Culture and Emotion Regulation
Emotion regulation skills may be culturally dependent. In a large-scale study, Harkness and colleagues (2007) found that U.S. families supported emotion regulation by supplying interesting and stimulating environments, whereas Dutch families focused on providing structure and routine. Italian families emphasized touch and tactile comfort, whereas Korean families prioritized physical well-being and routine (Harkness et al., 2007). Finally, Japanese American and European American infant-mother dyads showed similar person-oriented interaction and socialization behaviors, whereas Japanese infant-mother dyads showed more object-oriented interactions (Bornstein et al., 2012). Person-oriented interactions involve things like turn taking and face-to-face interactions, while object-oriented interactions involve the caregiver and infant interacting by both focusing on objects such as a toy. A variety of strategies across cultures can promote emotion learning and regulation (Friedlmeier et al., 2015).
Emotional Awareness
Along with emotion regulation, young infants and toddlers are beginning to develop a sense of emotional awareness , insight into their own emotional state and those of others (Figure 4.10). The process of recognizing and identifying our current affective state is called emotional labeling (Elsayed et al., 2021). Caregivers who assist toddlers with this skill help provide them with an important self-care tool to articulate and understand themselves (Nencheva et al., 2023). For example, a caregiver using emotional labeling might help a crying toddler identify their feelings and experiences by saying, “I know. You’re sad because big brother left to go to school, but he’ll be back.” Finally, recognizing emotions in others can help toddlers develop secondary emotions such as empathy and compassion (Spinrad & Gal, 2018).
Taken together, emotion regulation and emotional awareness are the building blocks for emotional intelligence, the ability to understand emotions and motivations in yourself and others (Mayer et al., 2011). Although many emotional milestones are accomplished in the first two years of life, there are many emotional tasks beyond a toddler’s ability. For instance, delay of gratification, or regulating happy and excited emotions to stay calm, will not start to develop until age four years. Knowing an infant’s or toddler’s developmental abilities and limits can aid caregivers and those who work with children, such as teachers and pediatric nurses or doctors, in promoting emotion development and regulation.
References
Abney, D. H., DaSilva, E. B., & Bertenthal, B. I. (2021). Associations between infant-mother physiological synchrony and 4- and 6-month-old infants’ emotion regulation. Developmental Psychobiology, 63 (6), e22161. doi.org/10.1002/dev.22161
Atkinson, N. H., Jean, A. D. L., & Stack, D. M. (2021). Emotion regulation from infancy to toddlerhood: Individual and group trajectories of full-term and very-low-birthweight preterm infants. Infancy, 26 (4), 570–595. doi.org/10.1111/infa.12405
Bornstein, M. H., Cote, L. R., Haynes, O. M., Suwalsky, J. T., & Bakeman, R. (2012). Modalities of infant-mother interaction in Japanese, Japanese American immigrant, and European American dyads. Child Development , 83 (6), 2073–2088. doi.org/10.1111/j.1467-8624.2012.01822.x
Brazelton, T. B. (1973). Neonatal Behavioral Assessment Scale. Spastics International Medical Publications. https://nidcap.org/wp-content/upload...1973-BNBAS.pdf
Ekman, P. (1992). An argument for basic emotions. Cognition and Emotion , 6 (3–4), 169–200. doi.org/10.1080/02699939208411068
Ekman, P. (1999). Basic emotions. In T. Dalgleish & M. J. Power (Eds.), Handbook of cognition and emotion, (pp. 45–60). John Wiley & Sons. doi.org/10.1002/0470013494.ch3
Elsayed, N. M., Vogel, A. C., Luby, J. L., & Barch, D. M. (2021). Labeling emotional stimuli in early childhood predicts neural and behavioral indicators of emotion regulation in late adolescence. Biological Psychiatry: Cognitive Neuroscience and Neuroimaging , 6 (1), 89–98. https://doi.org/10.1016/j.bpsc.2020.08.018
Feldman, R. (2007). On the origins of background emotions: from affect synchrony to symbolic expression. Emotion , 7 (3), 601–611. doi.org/10.1037/1528-35<IP_ADDRESS>1
Friedlmeier, W., Çorapçi, F., & Benga, O. (2015). Early emotional development in cultural perspective. In L. A. Jensen (Ed.), The Oxford handbook of human development and culture: An interdisciplinary perspective (pp. 127–148). Oxford University Press. doi.org/10.1093/oxfordhb/9780199948550.013.9
Gartstein, M. A., Hancock, G. R., & Iverson, S. L. (2018). Positive affectivity and fear trajectories in infancy: Contributions of mother-child interaction factors. Child Development, 89(5), 1519–1534. doi.org/10.1111/cdev.12843
Harkness, S., Super, C. M., Moscardino, U., Rha, J.-H., Blom, M. J. M., Huitrón, B., Johnston, C., Sutherland, M., Hyun, O.-K., Axia, G., & Palacios, J. (2007). Cultural models and developmental agendas: Implications for arousal and self-regulation in early infancy. Journal of Developmental Processes, 1 (2), 5–39. www.researchgate.net/publica..._Early_Infancy
Hay, D. F. (2019). Emotional Development from Infancy to Adolescence: Pathways to Emotional Competence and Emotional Problems. Routledge/Taylor & Francis Group. doi.org/10.4324/9781315849454
Izard, C. E. (1977). Differential emotions theory. In Human emotions (pp. 43–66). Springer. https://doi.org/10.1007/978-1-4899-2209-0_3
Izard, C. E. (1991). The psychology of emotions . Plenum Press. doi.org/10.1007/978-1-4899-0615-1
Kerr, M. L., Rasmussen, H. F., Smiley, P. A., Buttitta, K. V., & Borelli, J. L. (2021). The development of toddlers’ emotion regulation within the family system: associations with observed parent-child synchrony and interparental relationship satisfaction. Early Childhood Research Quarterly , 57 (4), 215–227. https://doi.org/10.1007/978-1-4899-2209-0_3
Kiel, N., Samdan, G., Wienke, A. S., Reinelt, T., Pauen, S., Mathes, B., & Herzmann, C. (2024). From co-regulation to self-regulation: Maternal soothing strategies and self-efficacy in relation to maternal reports of infant regulation at 3 and 7 months. Infant Mental Health Journal, 45 (2), 135–152. doi.org/10.1002/imhj.22098
Kim, B.-R., Stifter, C. A., Philbrook, L. E., & Teti, D. M. (2014). Infant emotion regulation: Relations to bedtime emotion availability, attachment security, and temperament. Infant Behavioral Development, 37 (4), 480–490. https://doi.org/10.1016/j.infbeh.2014.06.006
Lewis, M., & Sullivan, M. W. (2005). The development of self-conscious emotions. In A. J. Elliot & C. S. Dweck (Eds.), Handbook of competence and motivation , 185–201. psycnet.apa.org/record/2005-08058-011
Lewis, M., Sullivan, M. W., Stanger, C. & Weiss, M. (1989). Self development and self-conscious emotions. Child Development, 60 (1), 146–156. doi.org/10.2307/1131080
Mauss, I. B., Levenson, R. W., McCarter, L., Wilhelm, F. H., & Gross, J. J. (2005). The tie that binds? Coherence among emotion experience, behavior, and physiology. Emotion , 5 (2), 175–190. doi.org/10.1037/1528-35<IP_ADDRESS>
Mayer, J. D., Salovey, P., Caruso, D. R., & Cherkasskiy, L. (2011). Emotional intelligence. In R. J. Sternberg & S. B. Kaufman (Eds.), The Cambridge handbook of intelligence (pp. 528–549). Cambridge University Press. https://doi.org/10.1017/CBO9780511977244.027
Nencheva, M. L., Tamir, D. I., & Lew-Williams, C. (2023). Caregiver speech predicts the emergence of children’s emotion vocabulary. Child Development, 94 (3), 585–602. doi.org/10.1111/cdev.13897
Park, P. S., & Lewis, M. (2021). On the measurement of self-conscious emotions. Child Psychiatry & Human Development, 52 , 1164–1172. https://doi.org/10.1007/s10578-020-01094-2
Spinrad, T. L., & Gal, D. E. (2018). Fostering prosocial behavior and empathy in young children. Current Opinion in Psychology , 20 , 40–44. https://doi.org/10.1016/j.copsyc.2017.08.004
Thomas, J. C., Letourneau, N., Campbell, T. S., Tomfohr-Madsen, L., & Giesbrecht, G. F. (2017). Developmental origins of infant emotion regulation: Mediation by temperamental negativity and moderation by maternal sensitivity. Developmental Psychology , 53 (4), 611–628. dx.doi.org/10.1037/dev0000279
Tracy, J. L., & Randles, D. (2011). Four models of basic emotions: A review of Ekman and Cordaro, Izard, Levenson, and Panksepp and Watt. Emotional Review, 3 (4), 397–405. doi.org/10.1177/1754073911410747
Trevarthen, C. (2005). Action and emotion in development of cultural intelligence: why infants have feelings like ours. In J. Nadel & D. Muir (Eds.), Emotional development: Recent research advances (pp. 61–91). Oxford University Press. dx.doi.org/10.1093/acprof:oso...28845.003.0003
Watson, D., & Tellegen, A. (1985). Toward a consensual structure of mood. Psychological Bulletin , 98 (2), 219–235. doi.org/10.1037/0033-29<IP_ADDRESS>
Yik, M. S. M., Russell, J. A., & Barrett, L. F. (1999). Structure of self-reported current affect: Integration and beyond. Journal of Personality and Social Psychology , 77 , 600–619. doi.org/10.1037/0022-35<IP_ADDRESS>0


8.8: Osmosis, diffusion, and dialysis
29
Harper College Chemistry Department
Osmosis and Osmotic Pressure of Solutions
A number of natural and synthetic materials exhibit selective permeation , meaning that only molecules or ions of a certain size, shape, polarity, charge, and so forth, are capable of passing through (permeating) the material. Biological cell membranes provide elegant examples of selective permeation in nature, while dialysis tubing used to remove metabolic wastes from blood is a more simplistic technological example. Regardless of how they may be fabricated, these materials are generally referred to as semipermeable membranes.
Consider the apparatus illustrated in Figure 1 , in which samples of pure solvent and a solution are separated by a membrane that only solvent molecules may permeate. Solvent molecules will diffuse across the membrane in both directions. Since the concentration of solvent is greater in the pure solvent than the solution, these molecules will diffuse from the solvent side of the membrane to the solution side at a faster rate than they will in the reverse direction. The result is a net transfer of solvent molecules from the pure solvent to the solution. Transfer of solvent molecules through a semipermeable membrane is a process known as osmosis.
When osmosis is carried out in an apparatus like that shown in Figure 1 , the volume of the solution increases as it becomes diluted by accumulation of solvent. This causes the level of the solution to rise, increasing its hydrostatic pressure (due to the weight of the column of solution in the tube) and resulting in a faster transfer of solvent molecules back to the pure solvent side. When the pressure reaches a value that yields a reverse solvent transfer rate equal to the osmosis rate, bulk transfer of solvent ceases. This pressure is called the osmotic pressure ( Π ) of the solution. The osmotic pressure of a dilute solution is related to its solute molarity, M , and absolute temperature, T , according to the equation
where R is the universal gas constant.
If a solution is placed in an apparatus like the one shown in Figure 2 , applying pressure greater than the osmotic pressure of the solution reverses the osmosis and pushes solvent molecules from the solution into the pure solvent. This technique of reverse osmosis is used for large-scale desalination of seawater and on smaller scales to produce high-purity tap water for drinking.
In the process of osmosis, water moves through a semipermeable membrane from a less concentrated solution to a more concentrated solution. Osmotic pressure is the amount of pressure that must be applied to the more concentrated solution to cause osmosis to stop. If greater pressure is applied, the water will go from the more concentrated solution to a less concentrated (more pure) solution. This is called reverse osmosis. Reverse osmosis (RO) is used to purify water in many applications, from desalination plants in coastal cities, to water-purifying machines in grocery stores ( Figure 3 ), and smaller reverse-osmosis household units. With a hand-operated pump, small RO units can be used in third-world countries, disaster areas, and in lifeboats. Our military forces have a variety of generator-operated RO units that can be transported in vehicles to remote locations.
Examples of osmosis are evident in many biological systems because cells are surrounded by semipermeable membranes. Carrots and celery that have become limp because they have lost water can be made crisp again by placing them in water. Water moves into the carrot or celery cells by osmosis. A cucumber placed in a concentrated salt solution loses water by osmosis and absorbs some salt to become a pickle. Osmosis can also affect animal cells. Solute concentrations are particularly important when solutions are injected into the body. Solutes in body cell fluids and blood serum give these solutions an osmotic pressure of approximately 7.7 atm. Solutions injected into the body must have the same osmotic pressure as blood serum; that is, they should be isotonic with blood serum. If a less concentrated solution, a hypotonic solution, is injected in sufficient quantity to dilute the blood serum, water from the diluted serum passes into the blood cells by osmosis, causing the cells to expand and rupture. This process is called hemolysis. When a more concentrated solution, a hypertonic solution, is injected, the cells lose water to the more concentrated solution, shrivel, and possibly die in a process called crenation. These effects are illustrated in Figure 4 .